Time-dependent motions and the nonlinear bottom Ekman layer

The laminar bottom Ekman layer beneath a flow with finite relative vorticity is studied. First, the case with only a steady interior shear flow is reviewed, and then a case with a spatially uniform oscillating flow is superimposed. In both cases, the problem can be reduced to solving ordinary differential equations. The competition of two effects governs the results. The interior vorticity effectively modifies the rotation rate, but advection (especially vertically, due to Ekman pumping) tends to counteract the vorticity modification. Vertical advection keeps the time-dependent boundary layer well behaved for negative interior vorticities, but a boundary layer singularity can still exist at a single superinertial frequency when interior relative vorticity is positive.